With the advent of ever faster telecommunication data rates, it can be important to demonstrate clock speeds at more than approximately 1 THz not limited by, e.g., the optical pulse width, and to do so in a scalable approach. Soliton-effect pulse compression can offer a route to realize femtosecond pulses at multi-GHz repetition rates, in an integrated photonic chip, for example.
The generation of optical solitons can result from, e.g., a delicate balance of anomalous dispersion and positive Kerr nonlinearity (see, e.g., L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers, Phys. Rev. Lett. 45, 1095 (1980); and J. C. Bronski, M. Segev and M. I. Weinstein, Mathematical frontiers in optical solitons, Proc. Nat. Acad. Sci. 98, 12872 (2001)). Soliton-based pulse compression and propagation generally has enabled a large class of ultrafast applications ranging from, e.g., highly-efficient supercontinuum generation (see, e.g., J. M. Dudley, C. Finot, D. J. Richardson, and G, Millot, Self-similarity in ultrafast nonlinear optics, Nature Physics 3, 597 (2007); A. V. Gorbach and D. V. Skryabin, Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic crystal fibres, Nature Photonics 1, 653 (2007); F. Benabid, F. Couny, J. C. Knight, T. A. Birks, and P. St J. Russell, Compact, stable and efficient all-fibre gas cells using hollow-core photonic crystal fibres, Nature 434, 488 (2005); and J. M. Dudley, J. R. Taylor, Ten years of nonlinear optics in photonic crystal fibre, Nature Photonics 3, 85 (2009)), femtosecond frequency comb metrology (see, e.g., F. Couny, F. Benabid, P. J. Roberts, P. S. Light, M. G. Raymer, Generation and Photonic Guidance of Multi-Octave Optical-Frequency Combs, Science 318, 1118 (2007)) and spectroscopy, pulse shaping and regeneration towards terabit optical communications (see, e.g., M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Ultrafast waveform compression using a time-domain telescope, Nature Photonics 3, 581 (2009)), to, e.g., soliton squeezing for precision measurements (see, e.g., F. X. Kärtner, D. J. Doughery, H. A. Haus and E. P. Ippen, Raman noise and soliton squeezing, J. Op. Soc. Am. B 11, 1267 (1994)). The majority of these advancements have examined nonlinear optical fibers (see, e.g., D. G. Ouzounov, F. R. Ahmad, D. Miller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Generation of Megawatt Optical Solitons in Hollow-Core Photonic Band-Gap Fibers, Science 301, 1702 (2003); D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Optical rogue waves, Nature 450, 1054 (2007); D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Optical rogue waves, Nature 450, 1054 (2007); M. S. Kang, A. Nazarkin, A. Brenn and P. St. J. Russell, Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators, Nature Phys. 5, 276 (2009); M. Liao, C. Chaudhari, G. i Qin, Xin Yan, T. Suzuki, and Y. Ohishi, Tellurite microstructure fibers with small hexagonal core for supercontinuum generation, Optics Exp. 17, 12174 (2009); L. Fu, A. Fuerbach, I. C. M. Littler, and B. J. Eggleton, Efficient optical pulse compression using chalcogenide single-mode fibers, Appl. Phys. Lett. 88, 081116 (2006); and M. Foster, A. Gaeta, Q. Cao, and R. Trebino, Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires, Optics Exp. 13, 6848 (2005)), including, e.g., chalcogenide photonic crystal fibers, that can typically use pulse energies in the range of hundreds of pJ or more and can be several centimeters or more in length, due to the one to two orders of magnitude smaller Kerr nonlinearities (n2) and larger modal areas (Aeff) compared to integrated photonic chips, hardly amendable to monolithic integration, for example. Optical solitons have been examined in integrated channel waveguides theoretically and recently with experiments, although generally only with spectral-domain measurements (see, e.g., Q. Lin, Oskar J. Painter, and Govind P. Agrawal, Nonlinear optical phenomena in silicon waveguides: modeling and applications, Optics Exp. 15, 16604 (2007); R. El-Ganainy, S. Mokhov, K. G. Makris, D. N. Christodoulides, and R. Morandotti, Solitons in dispersion-inverted AlGaAs nanowires, Optics Exp. 14, 2277 (2006); J. I. Dadap, N.C. Panoiu, Xiaogang Chen, I-Wei Hsieh, Xiaoping Liu, Cheng-Yun Chou, E. Dulkeith, S. J. McNab, Fengnian Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, Jr, Nonlinear-optical phase modification in dispersion-engineered Si photonic wires, Optics Exp. 16, 1280 (2008)).
Laser diodes can be a possible route towards the integration of sub-picosecond optical sources. Recent advancements in monolithic mode-locking based on quantum dots have pushed the pulse widths down to sub-picoseconds (see, e.g., U. Rafailov, M. A. Cataluna, and W. Sibbett, Mode-locked quantum-dot lasers, Nature Photonics 1, 395 (2007); M. Kuntz, G. Fiol, M. Laemmlin, C. Meuer, D. Bimberg, High-Speed Mode-Locked Quantum-Dot Lasers and Optical Amplifier, Proc. IEEE 95, 1767 (2007); and B. R. Koch, A. W. Fang, O. Cohen, and J. E. Bowers, Mode-locked silicon evanescent lasers, Optics Exp. 15, 11225 (2007)), sometimes at the expense of the repetition rate and time-bandwidth product, based on, e.g., the trade-off optimization of the absorber/gain sections for each cavity length.
Photonic crystal lattices can have a group velocity dispersion (GVD; β2) of at least five orders of magnitude larger than in optical fibers opening the possibility of soliton compression in approximately 1-mm lengthscales for chip-scale integration. Recent studies have attempted a pulse compression where femtosecond pulses were injected but a broadened output pulse of approximately 1.1-ps was observed (see, e.g., T. J. Karle, Y. J. Chai, C. N. Morgan, I. H. White, and T. F. Krauss, Observation of pulse compression in photonic crystal coupled cavity waveguides, J. Lightwave Tech. 22, 514 (2004)) without Kerr nonlinearity and still generally requiring externally pre-chirped pulses, for example. Experimental investigation and development of Soliton dynamics in PhCs has been hindered due to the nonlinear absorption and linear losses until, e.g., recent breakthroughs in PhCs based on III-V semiconductors with mitigated nonlinear absorption (see, e.g., S. Combrié, Q. Vy Tran, C. Husko, P. Colman, and A. De Rossi, High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption, AppL Phys. Lett. 95, 221108 (2009); K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect, Optics Exp. 17, 7206 (2009)) as well as progress in fabrication quality and dispersion control (see, e.g., T. Baba, Slow light in photonic crystals, Nature Photonics 2, 465 (2008); and B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides, Nature Photonics 3, 206 (2009)). In parallel, theoretical studies have examined, e.g., the stability and dynamics of optical solitons in periodic structures (see, e.g., Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers To Photonic Crystals, Academic Press, San Diego, Calif., (2003); and X.-W. Chen, X.-S. Lin, and S. Lan, Subpicosecond pulse compression in nonlinear photonic crystal waveguides based on the formation of high-order optical solitons, Chinese Phys. 14, 366 (2005)), along with measurements on short-pulse propagation in k-space with mutual coupling between eigenstates (see, e.g., R. J. P. Engelen, Y. Sugimoto, H. Gersen, N. Ikeda, K. Asakawa, and L. Kuipers, Ultrafast evolution of photonic eigenstates in k-space, Nature Phys. 3, 401 (2007)).